Application of an Improved Trust-region Method to Rigid-Plastic Finite Element Analysis in Strip Rolling

Rigid-plastic finite element analysis (RPFEA) is an efficient and practical method to calculate rolling parameters in the strip rolling process. To solve the system of simulations equations involved in the RPFEA, a numerous of numerical methods, including the standard Newton-Raphson method, the modified Newton-Raphson method, and etc., have been proposed by different researchers. However, the computational time of the existed numerical methods can not meet the requirement of the online application. By tracking the computational time consumption for the main components in the standard Newton-Raphson method used in finite element analysis, it was found that linear search of damping factor occupies the most of the computational time. Thus, more efforts should be put on the linear search of damping factor to speed up the solving procedure, so that the online application of RPFEA is possible. In this paper, an improved trust-region method is developed to speed up the solving procedure, in which the Hessian matrix is forced to positive definite so as to improve the condition number of matrix. The numerical experiments are carried out to compare the proposed method with the standard Newton-Raphson method based on the practical data collected from a steel company in China. The numerical results demonstrate that the computational time of the proposed method outperforms that of the standard Newton-Raphson method and can meet the requirement of online application. Meanwhile the computational values of rolling force obtained by the proposed method are in good agreement with experimental values, which verifies the validity and stability of the proposed method.